Signal Detection Theory

Signal Detection Theory
Resources: Visual Perception
A Clinical Orientation Steven H. Schwartz
"Signal detection theory". Encyclopedia of
Psychology. FindArticles.com. 03 Jun, 2010.
http://findarticles.com/p/articles/mi_g2699/is_000
3/ai_2699000316/
adapted from Professor David Heeger

Gauri S Shrestha, M.Optom

Background
 The activity led to the development of the idea
of a threshold detection with stimulus
 even though the level of stimulation remained
constant, people were inconsistent in detecting
the stimulus
 There is no single, fixed value below which a
person never detects the stimulus and above
which the person always detects it
 An approach to resolving this dilemma is
provided by signal detection theory

Gauri S. Shrestha, M.Optom

Back ground
 This approach abandons the idea of a
threshold.
 Instead, the theory involves treating
detection of the stimulus as a decision-
making process
 Determinant of this process
 thenature of the stimulus,
 Sensitivity of a person to the stimulus, and
 cognitive factors


Back ground
 in a typical sensory experiment that involves a
large number of trials, an observer must try to
detect a very faint sound or light that varies in
intensity from clearly below normal detection
levels to clearly above.
 There are two possible responses, "Yes" and
"No." There are also two different possibilities
for the stimulus, either present or absent.
 when stimuli are difficult to detect, cognitive
factors are critical in the decision an observer
makes


The Human Threshold and Signal
detection theory
 We do not manifest a perfect threshold
 Due to decision criteria, attention, and internal
neural noise
 What is the Signal Detection Theory?
 Decision making takes place in the presence of some
uncertainty
 A model that addresses the role of these factors in
determining a threshold
 It provides a precise language and graphic notation for
analyzing decision making in the presence of uncertainty


SIGNAL DETECTION THEORY

 The precise notion/model of analysis
decision making process in the presence
of uncertainty


The basic idea behind signal detection
theory is that
 The level of neural noise fluctuates constantly.
When a faint stimulus, or signal, occurs, it
creates a neural response.
 The brain must decide whether the neural
activity reflects noise alone, or whether there
was also a signal.


Signal detection theory
 Neural Noise: Neurons are constantly sending
information to the brain, even when no stimuli are
present.
 The level of neural noise fluctuates constantly.
When a faint stimulus, or signal, occurs, it creates a
neural response.
 The brain must decide whether the neural activity
reflects
 noise alone, or also a signal
 When stimulus is difficult to detect= cognitive
factors are critical


Payoff Matrix: combination of rewards and
penalties for correct and incorrect decisions
 There is always a trade-off between the
number of Hits and False Alarms
 When a person is very willing to say that the
signal was present, that individual will show
more Hits, but will also have more False
Alarms.
 mathematical approaches to determine the
sensitivity of an individual for any given pattern
of Hits and False Alarms- index of sensitivity
(d‘)


contents

 Graphic interpretation of signal detection
theory
 Receiver Operating Characteristics (ROC
curve)
 Discriminability index (d')
 Examples


Signal Detection Theory
 Assumes there is random, fluctuating level of
background neural noise
 A stimulus’ signal is superimposed on this
noise
 This makes the observer’s task to differentiate:
 A. The signal and noise combination
 B. The noise alone


What To Remember…

 The noise is random and fluctuating
 The signal is constant
 The noise is always present and the signal is
superimposed
 The larger the signal, the easier it is for the
observer to detect


Internal response and internal noise

 External noise: environmental factor,
smugs, light, etc .
 Internal noise: Internal noise refers to the
fact that neural responses are noisy.
A doctor has a set of X detector neurons and
monitor the response of one of these neurons to
determine the likelihood that there is a X.
 These hypothetical X detectors will give noisy
and variable responses


Internal response and internal noise

 Internal response:
 determines the one’s impression about whether
or not a x factor is present.
 the state of the mind is reflected by neural
activity somewhere in the brain.
 This neural activity might be concentrated in just
a few neurons or it might be distributed across a
large number of neurons.
 refer to it as internal response


Detectability

d’

Internal response probability of occurrence curves for
noise-alone and for signal-plus-noise trials.


Detectability
 Definition: The difference between the
means of N and N + S
 Detectability increases as the distributions of
N and N + S become further apart
 With a very large ‘d,’ there is no uncertainty
whether the stimulus is present
 With a weak stimulus, the ‘d’ becomes much
smaller


Where does Confusion Occur?

Since the curves overlap, the internal response for a noise-alone trial
may exceed the internal response for a signal-plus-noise trial.
Vertical lines correspond to M.Optom
Gauri S. Shrestha, the criterion response

Information acquisition criterion
SIGNAL
R Present Absent
E
S YES HIT False alarm
HIT False alarm
P
O
N
NO Correct rejection
S Miss Correct rejection
E

Sensitivity= hit/hit+miss
Specificity= Correct rejection/CR+False alarm

Observer Responses
 False Positive (False Alarm)
 Observer reports stimulus when stimulus is not present
 Correct Reject
 Observer does not report stimulus when stimulus is
absent
 Hit
 Observer reports stimulus when stimulus is present
 Miss
 Observer does not report stimulus when stimulus is
present

Subject Criterion
 Lax Criterion vs. Strict Criterion
 Lax: Indicate a stimulus even with a great deal of
uncertainty (example: optometrist)
 Strict: Do not indicate a stimulus until they are
certain one is present (Example: hunter)
A Lax criterion results in a substantial number
of false positives, but very few misses
 A Strict criterion results in fewer hits, but a
lower number of false positives


Results of Observers’ Criterion

 Lax Criterion (Sensitive)
 High:Hits, False Positives
 Low: Misses, Correct Rejects

 Strict Criterion (specific)
 High:Misses, Correct Rejects
 Low: Hits, False Positive


Effect of shifting the criterion


The Receiver Operating Characteristic

 captures the various alternatives that are available
to the examiner in a single graph
 ROC curves are plotted with the false alarm rate on
the horizontal axis and the hit rate on the vertical
axis.
 if the criterion is high, then both the false alarm rate
and the hit rate will be very low. If we move the
criterion lower, then the hit rate and the false alarm
rate both increase.
 For any reasonable choice of criterion, the hit rate
is always larger than the false alarm rate, so the
ROC curve is bowed upward

A measure of goodness-of-fit is based
on the simultaneous measure of
sensitivity (True positive) and specificity
(True negative) for all possible cutoff
points.


Receiver Operating Characteristic (ROC)

a generalization of the set of potential
combinations of sensitivity and specificity
possible for predictors
 AUC values closer to 1 indicate the reliable
screening measure whereas values at .50
indicate the predictor is no better than chance


Varying the noise
 For stronger signals, the
probability of occurrence curve for
signal-plus-noise shifts right and
detection is easier

 The spread of the curves: The
separation between the peaks is
the same but the second set of
curves are much skinnier. Clearly,
the signal is much more
discriminable when there is less
spread (less noise) in the
probability of occurrence curves.


When Does Criterion Not Effect?
 d' = z(FA) - z(H)
 d’ =0
 Stimulus is so weak, no signal is produced
 Regardless of criteria, the proportion of hits
will match the proportion of false positives
 d’ = infinity
 Stimulus is easily distinguished and will
always be seen by the observer (No false
positives)


Discriminability index (d'):

 d' = separation / spread
 This number, d', is an estimate of the
strength of the signal.
 its value does not depend upon the criterion
the subject is adopting,
 it is a true measure of the internal response


How Do We Determine
Thresholds?
 Methods:
 Method of Ascending Limits
 Method of Descending Limits

 Staircase Method

 Method of Constant Stimuli

 Method of Adjustment

 Forced Choice Method


Method of Ascending Limits
 Stimulus is initially presented below threshold
 Stimulus is presented at increasingly intense
levels from presentation to presentation until
visible by observer
 Advantage:
 Relatively quick method
 Disadvantage:
 Participant Anticipation
 How to Avoid: Start each trial with stimulus of a
different intensity

Method of Descending Limits
 Reverse of Ascending Limits Method
 Stimulus initially presented clearly visible
and reduced until no longer seen
 Example: Visual Acuity
 Disadvantage:
 Patient Anticipation
 How to Avoid: start each trial a different level
of visibility


Staircase Method
 Combination of Ascending and Descending
 How Does It Work?
 Stimulus starts below threshold
 Presented in discrete steps of increasing visibility until
observer reports stimulus
 Visibility is reduced in discrete steps until stimulus can
no longer be detected
 Staircase is again reversed

 Thresholdis defined after three or four reversals
 Advantage: Quick and Reliable
 Example: Frequently used in Visual Field Testing


Staircase Method Demonstration


Method of Constant Stimuli
 Stimulus is randomly varied from
presentation to presentation
 Large number of stimuli presented at
each level of visibility
 Advantage:
 No Patient Anticipation
 Disadvantage:
 Time Consuming (not typically used
clinically)


Method of Adjustment

 Participants adjust intensity until the
stimulus is barely visible
 Advantage:
 Relatively quick
 Disadvantage:
 Patient criteria skews results


Forced Choice Method
 Minimizes the role of individual’s criterion
 Patient is forced to choose between several
alternative choices (one contains the
stimulus)
 A Different Number of Choices Can Be
Given:
2 Alternative Choice Method
 4 Alternative Choice Method

 Typically results in lower thresholds

Threshold Determination
 Threshold = Midway between 100% correct and
‘chance’
 Chance=percentage we expect observer to guess
correctly
 ‘Chance’ performance=50% correct
 Threshold=75% correct

 ‘Chance’ Performance=25% correct
 Threshold=62.5% correct


Thank you


Signal Detection Theory

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